Work out fixed point iteration instantly with clear inputs, formula shown and shareable results.
Fixed-point iteration repeatedly applies x ← g(x) until the value settles. The Banach condition |g'(x)| < 1 guarantees convergence, and smaller values converge faster.
Fixed point iteration
xₙ₊₁ = g(xₙ), converging when |g'(x)| < 1
Linear case
fixed point = b / (1 − a)
It converges to 3/(1 − 0.5) = 6.
Each step multiplies the error by roughly g', so a value below 1 shrinks the error and above 1 amplifies it.